Question

f the line passing through the points (1, a) and (5, −2) is parallel to the line passing through the points (2, 8) and (−5, a + 7), what is the value of a?

Answer 1

Answer:

$a=-6$

Step-by-step explanation:

Line 1:  (1, a) and (5, −2)

slope of the   line is

$slope = \frac{y_2-y_1}{x_2-x_1} =\frac{-2-a}{5-1} =\frac{-2-a}{4}$

Line 2:  (2, 8) and (−5, a + 7)

slope of the   line is

$slope = \frac{y_2-y_1}{x_2-x_1} =\frac{a+7-8}{-5-2} =\frac{a-1}{-7}$

when the lines are parallel then slopes are equal

$\frac{a-1}{-7} =\frac{-2-a}{4}$

cross multiply it

$4(a-1)=-7(-2-a)$

$4a-4=14+7a$

subtract 4a from both sides

$-4=14+3a$

$-18=+3a$

divide both sides by 3

$a=-6$